Abstract
We discuss various modifications of separability, precompactness and narrowness in topological groups and test those modifications in the permutation groups S(X) and \(S_{<\omega }(X)\).
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References
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Acknowledgements
The authors express their sincere thanks to Jan Pachl for his valuable comment on the implication \(\mathsf s_2^{\omega _1}{\mathsf {u}}_1{\mathsf {s}}_3^\omega \Rightarrow {\mathsf {u}}_1{\mathsf {s}}_2^{\omega _1}\) (proved in Lemma 3.31 of his book [5]).
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Banakh, T., Guran, I. & Ravsky, A. Generalizing separability, precompactness and narrowness in topological groups. RACSAM 115, 18 (2021). https://doi.org/10.1007/s13398-020-00945-w
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DOI: https://doi.org/10.1007/s13398-020-00945-w